The Dandy or its rival's not half posh (4)
I believe the answer is:
beau
'the dandy' is the definition.
(synonyms)
'rival's not half posh' is the wordplay.
I cannot quite see how this works, but
'posh' could be 'u' (abbreviation for upper-class - opposite to non-U) and 'u' is present in the answer.
The remaining letters 'bea' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'or its' acts as a link.
Can you help me to learn more?
(Other definitions for beau that I've seen before include "An old dandy like Brummel" , "Male admirer; dandy" , "young man" , "Fop; lover" , "An old boy friend like Brummel?" .)